Calculus

Sequences and Series Video Review Lessons

Sequences
• Fibonacci Numbers
• The Golden Ratio
• The Limit of a Sequence
• Determining the Limit of a Sequence
• The Squeeze and Absolute Value Theorems
Monotonic and Bounded Sequences
• Monotonic and Bounded Sequences
Infinite Series
• An Introduction to Infinite Series
• The Summation of Infinite Series
• Geometric Series
• Telescoping Series
Convergence and Divergence
• Properties of Convergent Series
• The nth-Term Test for Divergence
The Integral Test
• An Introduction to the Integral Test
• Examples of the Integral Test
• Using the Integral Test
• Defining p-Series
The Direct Comparison Test
• An Introduction to the Direct Comparison Test
• Using the Comparison Test
The Limit Comparison Test
• An Introduction to the Limit Comparison Test
• Using the Limit Comparison Test
• Inverting the Series in the Limit Comparison Test
The Alternating Series
• Alternating Series
• The Alternating Series Test
• Estimating the Sum of an Alternating Series
Absolute and Conditional Convergences
• Absolute and Conditional Convergence
The Ratio and Root Tests
• The Ratio Test
• Examples of the Ratio Test
• The Root Test
Polynomial Approximations of Elementary Functions
• Polynomial Approximation of Elementary Functions
• Higher-Degree Approximations
Taylor and Maclaurin Polynomials
• Taylor Polynomials
• Maclaurin Polynomials
• The Remainder of a Taylor Polynomial
• Approximating the Value of a Function
Taylor and Maclaurin Series
• Taylor Series
• Examples of the Taylor and Maclaurin Series
• New Taylor Series
• The Convergence of Taylor Series
Power Series
• The Definition of Power Series
• The Interval and Radius of Convergence
• Finding the Interval and Radius of Convergence: Part One
• Finding the Interval and Radius of Convergence: Part Two
• Finding the Interval and Radius of Convergence: Part Three
Power Series Representations of Functions
• Differentiation and Integration of Power Series
• Finding Power Series Representations by Differentiation
• Finding Power Series Representations by Integration
• Integrating Functions Using Power Series